Which is true for the entropy of a spontaneous reaction?

The correct option is ΔS₍ₛᵧₛₜₑₘ₎ + ΔS₍ₛᵤᵣ���ₒᵤₙ𝒹ᵢₙ𝓰ₛ₎ > 0.

To understand why this is correct, we refer to the Second Law of Thermodynamics, which governs the spontaneity of processes in nature. The law states that for any spontaneous process, the total entropy of the universe must increase.

The universe is defined as the system plus its surrounding environment. Therefore, the total change in the entropy of the universe ($\Delta S_{\text{universe}}$) is the sum of the change in entropy of the system ($\Delta S_{\text{system}}$) and the change in entropy of the surroundings ($\Delta S_{\text{surroundings}}$):

$$\Delta S_{\text{universe}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}$$

Since the Second Law requires that the entropy of the universe increases for a spontaneous process:
$$\Delta S_{\text{universe}}>0$$

By substituting the components of the universe into the inequality, we get the fundamental criterion for spontaneity:
$$\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}>0$$

This tells us that while the entropy change of the system or the surroundings individually can be negative, their sum must be positive for the overall process to occur spontaneously.